GoSam: automated multi-process scattering amplitudes at one loop

Transcription

1 GoSam: automated multi-process scattering amplitudes at one loop Gionata Luisoni Max Planck Institute for Physics Munich In collaboration with: G.Cullen, N. Greiner, G.Heinrich, P.Mastrolia, E.Mirabella, G.Ossola, F. Tramontano H. Van Deurzen, T.Peraro, J. Reichel, J. Schlenk, J.F.G. von Soden-Fraunhofen GoSam release: arxiv: [hep-ph] Amplitudes 2013, Ringberg Castle,

2 Outline GoSam: an overview Behind the curtains: some technical details Full NLO calculations Higgs + jets Conclusions & Outlook

3 OVERVIEW

4 Strategies for 1 loop Construction: Feynman diagrams Reduction: Integrand reduction On-shell tree-amplitudes Generalized unitarity Off-shell currents Tensor reduction

5 Tools for (automated) 1 loop computation Several strategies BlackHat Feynarts/Formcalc/LoopTools GoSam Helac-NLO MadGolem MadLoop Ngluon Numerical 1 loop Openloops Recola many tools: [Bern, Dixon, Febres Cordero, Höche, Ita, Kosower, Maître, Ozeren] [Hahn et al.] [Cullen, Greiner, Heinrich, Mastrolia, Ossola, Reiter, Tramontano, GL] [Bevilacqua, Czakon, van Hameren, Papadopoulos, Pittau, Worek] [Gonçalves-Netto, Lopez-Val, Mawatari, Plehn, Wigmore] [Hirschi, Frederix, Frixione, Garzelli, Maltoni, Pittau] [Badger, Biedermann, Uwer, Yundin] [Becker, Goetz, Reuschle, Schwan, Weinzierl] [Cascioli, Maierhöfer, Pozzorini] [Actis, Denner, Hofer, Scharf, Uccirati]

6 GoSam Meeting, January 2013 Gavin Cullen, Tiziano Peraro, Johannes Schlenk, Francesco Tramontano, Johann Felix v. Soden-Fraunhofen, Nicolas Greiner, Pierpaolo Mastrolia Giovanni Ossola, Joscha, Gudrun Heinrich, Hans van Deurzen, GL, Edoardo Mirabella

7 The GoSam Project: philosophy Golem (General One Loop Evaluator of Matrix elements) Samurai (Scattering Amplitudes from Unitarity based Reduction At Integrand level) Computation of amplitudes based upon: Algebraic generation of D-dimensional integrands via Feynman diagrams Reduction at the integrand level via D-dimensional extension of the OPP method and/or tensor integral calculation Generation on the fly of the full rational term

8 The GoSam Project: the codes GoSam: Python package to write code (fortran95) Code generation Diagram generation: QGRAF [Nogueira ] Algebra: FORM [Vermaseren ] SPINNEY [Cullen, Koch-Janusz, Reiter] Code generator: HAGGIES [Reiter] Generated code execution Loop integral reduction: SAMURAI [Mastrolia, Ossola, Reiter, Tramontano] GOLEM95 [Binoth, Cullen, Guillet, Heinrich, Pilon, Reiter] Scalar integral evaluation: AVHOLO [van Hameren] QCDLOOP [Ellis, Zanderighi] GOLEM95C [Cullen, Guillet, Heinrich, Kleinschmidt, Pilon, Reiter, Rodgers] LOOPTOOLS [Hahn et al.] Yellow codes distributed separately All codes in gosam-contrib package

9 BEHIND THE CURTAINS

10 Generation of the 1-loop code

11 Generation of the 1-loop code Full code for evaluation of 1-loop virtual amplitude

12 Generation of the 1-loop code gosam Full code for evaluation of 1-loop virtual amplitude

13 Generation of the 1-loop code Input Card gosam Monte Carlo Full code for evaluation of 1-loop virtual amplitude

14 Generation of the 1-loop code Input Card qraf Skeleton code: no expressions for amplitude gosam Monte Carlo Full code for evaluation of 1-loop virtual amplitude

15 Generation of the 1-loop code Input Card qraf Skeleton code: no expressions for amplitude gosam form haggies Monte Carlo Full code for evaluation of 1-loop virtual amplitude

16 Generation of the 1-loop code Input Card qraf Skeleton code: no expressions for amplitude gosam form haggies Monte Carlo Full code for evaluation of 1-loop virtual amplitude [Vermaseren]

17 Numerator construction with: Numerator constructed from algebraic expression in terms of Feynman diagrams: ;

18 Making the evaluation faster To reduce the number of calls to the reduction program, diagrams are collected both horizontally and vertically in the number of propagators: # propagators.....

19 Making the evaluation faster To reduce the number of calls to the reduction program, diagrams are collected both horizontally and vertically in the number of propagators: # propagators Diagsum

20 Making the evaluation faster To reduce the number of calls to the reduction program, diagrams are collected both horizontally and vertically in the number of propagators: # propagators

21 Making the evaluation faster To reduce the number of calls to the reduction program, diagrams are collected both horizontally and vertically in the number of propagators: # propagators Grouping

22 Diagsum Diagrams sharing identical denominators can be summed before the algebraic processing: Sum diagrams which have different tree-part:

23 Diagsum Diagrams sharing identical denominators can be summed before the algebraic processing: Sum diagrams which have different tree-part Sum diagrams with same loop but different particles in loop:

24 Grouping Group numerators of diagrams sharing same cuts Structure of diagrams is analyzed Detect diagrams sharing same proparators If needed apply a shift to the loop momentum

25

26 Numerator construction Construct expression suitable for both by factoring out loopmomentum dependent part: : coefficient depending only from constants and ffexternal kinematical variables (abbreviation) written in optimized form recycling common subexpressions evaluated once per phase-space point : some function of the loop momentum

27 Reduction method 1: Samurai [Mastrolia, Ossola, Reiter, Tramontano] Factorized numerator reduced with SAMURAI: OPP reduction algorithm D-dimensional extension [Ossola, Papadopoulos, Pittau] [Ellis, Giele, Kunszt, Melnikov] : are polynomials in the components of and in

28 Reduction method 1: Samurai [Mastrolia, Ossola, Reiter, Tramontano] Factorized numerator reduced with SAMURAI: For each cut define basis of four massless vectors and write Subtract higher point residues to detemine lower ones

29 Reduction method 1: Samurai [Mastrolia, Ossola, Reiter, Tramontano] Factorized numerator reduced with SAMURAI: Coefficient of polynomials via DFT [Mastrolia, Ossola, Papadopoulos, Pittau]

30 Reduction method 2: Golem95 Reconstruct tensor coefficient of factorized numerator by successive derivative: derive: computes the numerator by expanding in a Taylor series one-to-one correspondence between derivatives at coefficients of the tensor integrals and the In general slightly slower but, together with tensor integral library, great stabiliy: perfect as a rescue system!

31 D-dim. Integrand Reduction via Laurent Expansion The coefficients of the master integrals obtained from a Laurent expansion of the integrand on the multiple cuts Structure of multiple cut residues is process-independent integrand subtraction replaced by corrections to the coefficients obtained with the Laurent expansion Advantage: a "lighter" reduction algorithm where fewer coefficients need to be computed e.g. quintuple cut not needed [Mastrolia, Mirabella, Peraro] [Forde; Kilgore; Badger] [Ossola, Papadopoulos, Pittau] quadruple cut decoupled from triple-, double-, and single-cut.

32 Reduction method 3: Ninja Implemented within GoSam using Ninja: Process for the Laurent expansion providing: relevant coefficients of the expansion needed for the quadruple cuts the coefficients of the parametric expansion at needed for all the triple, double, and single cuts. Ninja is a C++ library that: performs the Laurent expansion semi-numerically through a simplified polynomial-division algorithm determines the coefficients combines coefficients and master integrals [Mastrolia, Mirabella, Peraro]

33 Rational part: R 2 treatment NO special action is necessary for R 2 Nevertheless two solutions possible: R 2 implicit: - terms kept into numerator expression and processed with other terms by SAMURAI/GOLEM95 R 2 explicit: - terms separated and computed analytically during algebraic reduction of the numerator useful to detect large cancellation between cutconstructible part and R 2

34 Running time reduction strategies Start reduction = 0,2,21,22 0,2 yes 21,22 Samurai Ninja reduction = 0 or test ok yes End

35 Running time reduction strategies Start Tensorial reconstruction reduction = 0,2,21,22 0,2 yes 21,22 no reduction = 3,4 no Golem95C Samurai Ninja reduction = 0 or test ok no yes End

36 Running time reduction strategies Start Tensorial reconstruction reduction = 0,2,21,22 0,2 yes 21,22 no reduction = 3,4 yes no Golem95C Samurai Ninja Samurai (recon. numerator) reduction = 0 or test ok yes no reduction = 3 or test ok yes no End

37 W+jets W+0 jets Subrocesse # Initial Diagrams # Diagrams after sum # Groups Timing < 0.1 ms W+1 jet < 0.5 ms W+2 jets ms W+3 jets ms W+4 jets Color 4195 & helicity summed 360????? ms

38 W+jets W+0 jets Subrocesse # Initial Diagrams # Diagrams after sum # Groups Timing < 0.1 ms W+1 jet < 0.5 ms W+2 jets ms W+3 jets ms W+4 jets Color 4195 & helicity summed 360????? ms WORLD RECORD: W+5 jets by the BlackHat collaboration [Bern, Dixon, Febres Cordero, Höche, Ita, Kosower, Maître, Ozeren]

39 Croatian: neidentifikovani leteći objekat (NLO) FULL NLO?!

40 FULL NLO!!

41 NLO Calculation For a full NLO calculation other ingredients are needed: Integrator / Event generator One-loop amplitudes Virtual Tree-level amplitudes Born Real AUTOMATION Important : -Self-organization -Avoid human mistake -Process indep. framework

42 NLO Calculation For a full NLO calculation other ingredients are needed: Integrator / Event generator One-loop amplitudes Virtual Tree-level amplitudes Born Real AUTOMATION Important : -Self-organization -Avoid human mistake -Process indep. framework BLHA [BLHA, arxiv: [hep-ph]]

43 GoSam with external MC Via BLHA Interface GoSam + MadGraph4 + MadDipole + MadEvent Interfaced via add-hoc interface Succesfully used to compute: W + W jets bbbb production X X jet γ + γ + 1 jet GoSam + POWHEG Development phase completed Finalizing test phase [Nason, Oleari, Tramontano, G.L. in preparation] GoSam + SHERPA [Schönherr, Tramontano, Winter, G.L. in preparation] Possible since Sherpa (March 2012) : [--enable-lhole] Little additional patch needed for parameter communication Packages publicly available at: Succesfully used to compute H+2 jets in gluon-gluon fusion Graviton + 1 jet in ADD model [Greiner, Heinrich, Mastrolia, Ossola, Reiter, Tramontano] [Melia et al.] [Greiner, Guffanti, Reiter, Reuter] [Binoth Guillet ] [Cullen, Greiner, Heinrich] [Gehrmann, Greiner, Heinrich] Soden-Fraunhofen, Tramontano, G.L. ] [van Deurzen, Greiner, Mastrolia, Mirabella, Ossola, Peraro, von [Greiner, Heinrich, Reichel, von Soden-Fraunhofen in preparation]

44 GoSam+Sherpa Process Packages Actual status of freely available processes: Process Number of extra jets W 0,1,2 3 Z 0,1 2 W+ b b (massive b s) 0 1 γ - 0,1,2 H - 0,1,2 W + W - 0 1,2 + 0 loop-induced W + W W + W - b b - 0 t t - 0,1 H t t - 0,1 Available on:

45 + =?? HIGGS + JETS

46 Higgs+jets: Motivation Higgs-like boson discovered last July: is it the Higgs? Need to determine properties by studying all possible production/decay channels and background processes Many precise studies ongoing e.g contamination of vbf sample by ggf events [Gangal, Tackmann ; NLO MC in YR3] Vector boson fusion Gluon-gluon fusion Started systematic computation of QCD corrections to H+jets using GoSam

47 Higgs+jets: the higher rank issue For any 1-loop amplitude Rank: = # powers of loop momentum in numerator in SM with renormalizable gauges: in SM with effective gluon-gluon-higgs vertex: Adapt reduction programs Samurai and Golem95 to deal with higher rank loop integrals [Mastrolia, Mirabella, Peraro; van Deurzen, Mastrolia] [Guillet, Heinrich, von Soden-Fraunhofen ongoing]

48 Higgs+jets: NLO virtual corrections H+0 jets Processes # Initial Diagrams # Diagrams after sum # Groups Timing < 1 ms

49 Higgs+jets: NLO virtual corrections H+0 jets Processes # Initial Diagrams # Diagrams after sum # Groups Timing < 1 ms H+1 jets ms 7 ms

50 Higgs+jets: NLO virtual corrections H+0 jets H+1 jets H+2 jets Processes # Initial Diagrams # Diagrams after sum # Groups Timing < 1 ms 3 ms 7 ms 9 ms 15 ms 56 ms 316 ms 12 rank 6 pentagons

51 Higgs+2jets [van Deurzen, Greiner, Luisoni, Mastrolia, Mirabella, Ossola, Peraro, von Soden-Fraunhofen, Tramontano] Using BLHA interface for GoSam+Sherpa Agreement with MCFM (v6.4) [Campbell, Ellis, Williams]

52 Higgs+jets: NLO virtual corrections H+0 jets Processes # Initial Diagrams # Diagrams after sum # Groups Timing < 1 ms H+1 jets H+2 jets H+3 jets ms 7 ms 9 ms 15 ms 56 ms 316 ms 290 ms 600 ms ms ms Color & helicity summed

53 Higgs+jets: NLO virtual corrections H+1 jets H+2 jets H+3 jets < 1 ms ms ms ms 15 ms ms 60 rank 7 hexagons ms ms ms ms ms

54 Higgs+3jets: virtual contribution Rotating a phase-space point around the y axis

55 Towards NLO Transverse momentum distributions of jets:

56 pp H t t + 1 NLO Example using GoSam+Ninja: H t t computed more than 10 years ago Relevant for determination of Higgs-top Yukawa coupling Two different masses: m H, m T In gluonic channel 51 hexagons: [Dittmaier et al.; Reina et al.] H t t +1 jets Processes # Initial Diagrams # Diagrams after sum # Groups # Helic. Timing ms 4160 ms Color & helicity summed

57 pp H t t + 1 NLO Example using GoSam+Ninja:

58 Outlook: Towards GoSam-2.0 In parallel with phenomenology studies, continuous phase of code development Plan to release GoSam-2.0 later this year with Faster code generation Lighter executables thanks to improved optimization using FORM > 4 Faster and stabler evaluation of vitual amplitude at running time New reduction algorithm: Ninja Extended and more flexible interface with external MC [Vermaseren]

59 Conclusions GoSam: program for the automatic computation of 1-loop amplitudes algebraic generation of D-dimensional integrands via Feynman diag. reduction using integrand reduction and tensor integrals on-the-fly computation of full rational term Interfaced successfully to several external MC for pheno studies computation of H+jets processes in gluon-gluon fusion Preliminary results for GoSam+Ninja: d-dim. integrand reduction via Laurent expansion Outlook: Code improvements to make computation faster and lighter : GoSam-2.0 Phenomenology studies for next LHC run